Polinomial chaos expansion applied to limit state functions

Abstract

In structural projects, ensuring system performance within the established specifications with a maximum level of safety and taking into account the economic constraints of the project is one of the main objectives of structural design. The risks to which any physical system is subjected are called failure probability and are assessed by applying structural reliability analysis methods. The objective of the structural reliability analysis is to ensure that the strength of the elements of the structure is greater than the imposed strength demand over the service life of each of the structural elements. Structural design variables are physical quantities in structural reliability and are considered random, and can be represented in a random vector. The failure probability of a structure is obtained from the evaluation of the uncertainties inherent to the physical variables of the project, through the probability distributions of the random variables. The objective of this work was the application of polynomial chaos expansion to evaluate the failure probability in limit state functions found in the literature using numerical simulation, in order to decrease the sample size for each random variable compared to those needed using Monte Carlo simulation. This research showed that the difference between the sample size between polynomial chaos expansion and Monte Carlo simulation is 5%, saving time and computational effort.